Simplify the number using the imaginary unit i. (1 point) Responses Image with alt text: 2 square root -7 Image with alt text: -2 square root -7 Image with alt text: i square root 28
The simplified form of i square root 28 is 2 square root 7 i.
To simplify the number using the imaginary unit i, you need to simplify the expression involving the square root of a negative number.
In this case, we have the expression √28. To simplify this, we can break it down into two parts:
1. Factorize the number inside the square root, if possible.
2. Simplify the square root using the property of imaginary unit i.
Now, let's start with the first step.
The number 28 can be broken down into its prime factors: 2 * 2 * 7. So, we have √(2 * 2 * 7).
Next, let's move on to the second step.
According to the property of the imaginary unit i, √(-1) = i. Therefore, we can write √(2 * 2 * 7) as √(2 * 2 * 7 * -1).
Now, we can use the property of square roots to split it into two separate square roots:
√(2 * 2 * 7 * -1) = √(2 * 2 * 7) * √(-1).
Simplifying further, we get:
= 2 * √(7) * i.
Therefore, the simplified form of i√28 is 2√7i.
To simplify the number using the imaginary unit i, we can convert the number to its simplest form in the form of a + bi.
- In the first option, 2√(-7), we need to simplify the square root of -7. Since the square root of a negative number is not a real number, we can express it as 2√7i. So, the simplified form is 2√7i.
- In the second option, -2√(-7), we can simplify it in a similar way. We simplify the square root of -7 as √7i, and since the negative sign applies to the whole expression, the simplified form is -2√7i.
- In the third option, i√28, we need to simplify the square root of 28. Simplifying it gives us 2√7i. So, the simplified form is 2√7i.
Therefore, the correct option is: Image with alt text: 2 square root 7i